Fundamental inefficiencies in the lasing process of any laser system result in some fraction of the pump power being left behind as waste heat in the lasing medium. This heat causes a change in the index of refraction and thermal expansion of the lasing medium. The wavefront of the extraction beam is distorted if it is passed through a lasing medium with non-uniform temperature distribution. The specific parameters of the pump, extraction, cooling and gain medium geometry determine the nature of such wavefront distortion.
Thermally-induced distortion generated in side-pumped lasers can be substantially eliminated with simple focus correction. However, the non-uniform heat distribution in end-pumped lasers is inherently non-uniform, so that the correction of thermally-induced distortion is more complex than simple focus correction. In this case, the distortion may be represented by a combination of focus and higher-order spherical aberrations.
An optical wavefront that is a surface of revolution can be defined as the sum of its oscillating sphere plus higher order terms by means of the following relationship, taking the z-axis as the axis of revolution, ##EQU1## where c=1/radius of curvature and s=x.sup.2+ y.sup.2. Also, B.sub.1 B.sub.2 and B.sub.3 are the aspheric deformation constants. The B.sub.i constants represent the higher-order spherical aberrations while the first term in this wavefront expansion relationship represents the focus. In a conventional resonator, that is, one with a combination of spherical and flat surfaces, only the first term in the wavefront distortion expansion can be corrected.
The spherical aberrations reduce the output beam quality as well as the laser efficiency. Laser efficiency is reduced because the distortion diffracts power out of the fundamental mode volume of the laser cavity, thereby causing significant round-trip losses. The degree to which the efficiency is reduced depends on the gain, as well as the magnitude and distribution of the aberration. In low gain continuous-wave (CW) lasers, the aberrations can dominate laser performance above output powers of a few Watts.
Correction of thermally-induced aberration has not been a problem with most laser systems, whether side-pumped or end-pumped. As indicated above, for uniformly pumped side-pumped lasers, any thermally-induced distortion is easily suppressed with simple focus correction. End-pumped laser systems have been limited in power by the difficulty of transfer of significant pump energy to the small mode volume within the gain medium, so that the generation of heat within the gain medium has not been sufficient to cause significant thermally-induced aberration.
Recent advances in the art have permitted increased pump power transfer in end-pumped systems to levels that generate enough heat in the gain medium to cause significant thermally-induced aberration. As indicated above, this distortion is difficult to correct, since it includes higher-order spherical aberrations. Simple focus adjustment cannot adequately suppress this distortion. The only known attempt at correcting this type of distortion in end-pumped laser systems involves shaping steeply curved spherical surfaces on each end of an end-pumped laser rod in the laser system optical cavity.
One end surface is made concave and the other convex to provide a degree of under-corrected third-order spherical aberration that largely cancels the thermally-induced aberration. This method of correction is simple, in that only spherical surfaces are necessary, and efficient, in that no additional elements are required. However, this method has several disadvantages. One disadvantage is that the steeply-curved spherical surfaces that are required for the rod ends cause additional loss in the optical cavity since the Fresnel reflections cannot be efficiently coupled back into the laser mode region of the rod.
Another reason is that the under-corrected third-order spherical aberration only approximates the thermally-induced aberration, so that correction is only partial at best. Another reason is that the short radii of the spherical surfaces are difficult to fabricate. Still another reason is that the curved rod surfaces affect the distribution of pump energy. A further reason is that it is more difficult to apply coatings to steeply curved surfaces and the performance of such coatings is degraded.